I've used webbing, and I've also made my own from linen and pillow ticking. In the photo section, I have an example of both. The pouch for the Tennessee Rifle has a webbing strap, whereas the pouch for the Smoothbore has a strap made of linen.
Basically, I take a strip of linen of the correct length, and at least twice as wide as I want my strap to be. Then, I fold the edges in towards each other, so that I have both edges together going down the center of the fabric.
Next, I take another piece of linen, or ticking (or you could use another materil of your choice, and I fold it in the same manner, and then lay it on top of the first piece so that the folded edges on each strap are now facing each other.
Then, I simply sew down the edge on each strap with linen thread. You could put leather ends on it if you wish, or even another material, or fold the last inch or so back against itself...
Not hard to do, but it will take a little time (I sew by hand). You can dye the linen in walnut hull dye.....use the dye cold for a mild color, and use it warm for a deeper color...
Anyway, this is just one method, but I like the end result. Although my Tennessee Rifle has a pouch with a webbing strap, I made the strap for the powder horn out of linen and ticking utilizing the method that I just described.